Physics 208-02 – Introductory Physics II

Solution Set 5

Nazareth College

Department of Chemistry & Biochemistry

Robert F Szalapski, PhD – Adjunct Lecturer

www.CallMeDrRob.com

Spring 2012

## § Chapter 12, Problem 7

Calculate the percent error made over a distance of one mile by the “five-second rule” for estimating the distance of a lightning strike for the temperatures indicated. (The rule states a five-second delay between the flash of lightning and the ensuing sound of thunder for every mile from the strike treating the delay for the travel of light as negligible.)

### § (a)

.

Compute the speed of sound at .

The distance traveled in five seconds is then

The error is then approximately

### § (b)

.

Compute the speed of sound at .

The distance traveled in five seconds is then

The error is then approximately

## § Chapter 12, Problem 10

If two firecrackers produce a sound level of when fired simultaneously at a certain place, what will the sound level be if only one is fired? (Hint, intensities add, not sound levels).

There is a shortcut here. Note the following.

## § Chapter 12, Problem 12

A casette player is said to have a signal to noise ratio of , whereas for a CD player it is . What is the ration of intensities for each device?

For the cassette player:

For the CD player:

That’s an improvement by a factor of 5,000 in terms of the intensity ratio!

## § Chapter 12, Problem 14

A sound wave strikes an eardrum whose area is .

### § 0.1. (a)

How much energy is absorbed by the eardrum per second?

Begin by computing the intensity which is power per unit area:

Now compute the power by multiplying by the area:

Notice the units. Power is energy per unit time.

### § 0.2. (b)

How long would it take your eardrum to receive a total energy of ?

If you don’t remember the equations, just pay attention to the units.

## § Chapter 12, Problem 15

Expensive amplifier A is rated at while the more modest amplifier B is rated at .

### § (a)

Estimate the sound level in decibels that you would expect at a point from a loudspeaker connected in turn to each amplifier.

While loudspeakers are somewhat directional, our best estimate without more information is that the energy is distributed over a spherical surface. For amplifier A:

For amplifier B:

### § (b)

Will the expensive amp sound twice as loud as the cheaper one?

No, it will not. It will sound louder by approximately

## § Chapter 12, Problem 24

A string on a violin has a fundamental frequency of . The length of the vibrating portion is with a mass of . Under what tension must the string be placed?

With the wave speed given by

and the fundamental frequency given by

we may write

## § Chapter 12, Problem 39

A piano tuner hears one beat every when trying to adjust two strings, one of which is sounding . How far off in frequency is the other string?

We are given the beat period, so use it to calculate the beat frequency.

So the frequency of the second string differs from the first by . In other words, it is either or .

## § Chapter 12, Problem 49

The predominant frequency of a certain fire engine’s siren is when at rest.

### § (a)

What frequency do you detect when you move toward the fire engine?

The equation for the Doppler shift is given by

In this case the speed of the source is zero, so

Moving towards the source we anticipate the pitch will increase, so choose the addition rather than subtraction where there is the symbol. Then

### § (b)

What frequency do you detect when you move away from the fire engine?

Follow exactly the same logic as part (a) with the change that because we expect the pitch to drop when moving away from the source. Then

## § Chapter 12, Problem 53

A bat at rest send out ultrasonic sound waves at and receives them returned from an object moving directly away from it at . What is the received frequency?

Start with the equation for the Doppler shift given by

First the object acts as the observer moving away at , and we choose in the numerator because the pitch will drop. The object now acts as a source with , and we choose because the pitch will drop with the source moving away. Hence

## § Chapter 12, Problem 55

In one of the original Doppler experiments a tuba was played on a moving flat train car at a frequency of , and an identical tuba at rest in the station played the same tone. What beat frequency was heard as the train approached the station at ?

First compute the Doppler shifted frequency with a moving source choosing subtraction in the denominator for increased pitch.

Then